package agents.anac.y2015.Phoenix.GP;/* This file is part of the jgpml Project. * http://github.com/renzodenardi/jgpml * * Copyright (c) 2011 Renzo De Nardi and Hugo Gravato-Marques * * Permission is hereby granted, free of charge, to any person * obtaining a copy of this software and associated documentation * files (the "Software"), to deal in the Software without * restriction, including without limitation the rights to use, * copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the * Software is furnished to do so, subject to the following * conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR * OTHER DEALINGS IN THE SOFTWARE. */ import static agents.anac.y2015.Phoenix.GP.MatrixOperations.*; import java.util.Arrays; import agents.Jama.Matrix; /** Squared Exponential covariance function with Automatic Relevance Detemination * (ARD) distance measure. The covariance function is parameterized as: *
* k(x^p,x^q) = sf2 * exp(-(x^p - x^q)'*inv(P)*(x^p - x^q)/2) *
* where the P matrix is diagonal with ARD parameters ell_1^2,...,ell_D^2, where * D is the dimension of the input space and sf2 is the signal variance. The * hyperparameters are: *
* [ log(ell_1)
* log(ell_2)
* .
* log(ell_D)
* log(sqrt(sf2))]
*/
public class CovSEard implements CovarianceFunction {
private int D;
private int numParameters;
private Matrix K=null;
/**
* Creates a new PhoenixAlpha.CovSEard PhoenixAlpha.CovarianceFunction
with respect
* to the hyperparameter with index
* @param inputDimension muber of dimension of the input
*/
public CovSEard(int inputDimension){
this.D = inputDimension;
numParameters = D+1;
}
/**
* Returns the number of hyperparameters of
of hyperparameters
* @param X input dataset
* @param Xstar test set
* @return [K(Xstar,Xstar) K(X,Xstar)]
*/
public Matrix[] compute(Matrix loghyper, Matrix X, Matrix Xstar) {
if(X.getColumnDimension()!=D)
throw new IllegalArgumentException("The number of dimensions specified on the covariance function "+D+" must agree with the size of the input vector"+X.getColumnDimension());
if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters)
throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters);
final Matrix ell = exp(loghyper.getMatrix(0,D-1,0,0)); // characteristic length scales
final double sf2 = Math.exp(2*loghyper.get(D,0)); // signal variance
double[] a = new double[Xstar.getRowDimension()];
Arrays.fill(a,sf2);
Matrix A = new Matrix(a,Xstar.getRowDimension());
Matrix diag = new Matrix(D,D);
for(int i=0; iPhoenixAlpha.CovSEard
* @return number of hyperparameters
*/
public int numParameters() {
return numParameters;
}
/**
* Compute covariance matrix of a dataset X
* @param loghyper column Matrix
of hyperparameters
* @param X input dataset
* @return K covariance Matrix
*/
public Matrix compute(Matrix loghyper, Matrix X) {
if(X.getColumnDimension()!=D)
throw new IllegalArgumentException("The number of dimensions specified on the covariance function "+D+" must agree with the size of the input vector"+X.getColumnDimension());
if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters)
throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters);
final Matrix ell = exp(loghyper.getMatrix(0,D-1,0,0)); // characteristic length scales
final double sf2 = Math.exp(2*loghyper.get(D,0)); // signal variance
Matrix diag = new Matrix(D,D);
for(int i=0; iidx
*
* @param loghyper hyperparameters
* @param X input dataset
* @param index hyperparameter index
* @return Matrix
of derivatives
*/
public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index){
if(X.getColumnDimension()!=D)
throw new IllegalArgumentException("The number of dimensions specified on the covariance function "+D+" must agree with the size of the input vector"+X.getColumnDimension());
if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters)
throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters);
if(index>numParameters()-1)
throw new IllegalArgumentException("Wrong hyperparameters index "+index+" it should be smaller or equal to "+(numParameters()-1));
Matrix A=null;
final Matrix ell = exp(loghyper.getMatrix(0,D-1,0,0)); // characteristic length scales
final double sf2 = Math.exp(2*loghyper.get(D,0)); // signal variance
// noise variance
if(K.getRowDimension()!=X.getRowDimension() || K.getColumnDimension()!=X.getRowDimension()){
Matrix diag = new Matrix(D,D);
for(int i=0; i